A blazed grating is an optical element having a sawtooth blazed surface, which includes a plurality of light-transmitting slopes. A light-converging device having a blazed grating on its surface is disclosed in Non-Patent Document 1 and Patent Document 1.
With reference to FIG. 10 and FIG. 11, a conventional example of a light-converging device will be described.
The light-converging device shown in FIG. 10 comprises a substrate 1, which is formed of a transparent material such as plastic and has surfaces 1a and 1b. The substrate 1 has a lens shape which is symmetric around its optical axis, and has a grating 1G formed on the surface 1b thereof, the grating 1G having a sawteeth-shaped cross section. The lens surfaces 1a and 1b of the light-converging device constitute a sphere or non-sphere, with its center axis being the optical axis L. On the surface 1b, the plurality of light-transmitting slopes composing the grating 1G each have an annular shape whose center axis is the optical axis L, and are arrayed in a radial direction. Thus, steps of the grating are formed in concentric circles centered around the optical axis.
Light 2 which enters the substrate 71 is refracted by the surface 1a, and thereafter simultaneously receives refraction and diffraction at the surface 1b on which the grating 1G is formed. Light 3 going out from the light-converging device is converged on a detection surface 4.
Next, with reference to FIG. 11, the principle of diffraction by the lens surface 1b of the light-converging device shown in FIG. 10 will be described. For simplicity, FIG. 11 illustrates the surface 1b as being planar.
The device shown in FIG. 11 has a substrate 1 having a grating 1G formed on a surface 1b thereof, the grating 1G having a sawteeth-like cross section. The substrate 1 has a refractive index n. The grating 1G has a pitch Λ. The grating 1G diffracts light 2 of the wavelength λ, thus generating diffracted light such as 1st-order diffracted light 3 and 2nd-order diffracted light 3″.
For simplicity, assuming that the incident angle of the light 2 (i.e., the angle between the normal of the rear face of the substrate 1 and the axis of the light 2) is zero, the diffraction angle θ of the qth-order diffracted light (i.e., the angle between the normal and the diffracted light) is expressed by (eq. 1) below.sin θ=qλ/Λ  (eq. 1)
Herein, q is an integer representing the order of the diffracted light.
In the case of 0th-order light 3′, q=0, and the diffraction angle θ is zero. Generally speaking, −1st-order diffracted light and −2nd-order diffracted light are also generated on opposite sides of the 0th-order light 3′. However, since the grating 1G has a sawteeth-like cross section, diffracted light of any − order will be weakened, whereas diffracted light of any + order will be intensified. When a step height d in the cross section of the grating 1G satisfies (eq. 2) below, the diffraction efficiency of the qth-order diffracted light becomes maximum.d=|qλ/(n−1)|  (eq. 2)
Herein, n is the refractive index of the substrate (transparent medium), and λ is the wavelength of the incident light 2. Note that the pitch Λ does not need to be constant across the surface of the substrate 1, and the pitch Λ may be a mathematical function of position on the substrate 1. By varying the pitch Λ as a mathematical function of position, it becomes possible to adjust the diffraction angle in accordance with the outgoing position from the substrate 1. By doing so, and assisted also by the spherical shape of the surfaces 1a and 1b, etc., it becomes possible to converge the diffracted light 3 at one point.
Next, with reference to FIG. 12 and FIG. 13, another conventional technique will be described. This conventional technique has a construction as taught in Patent Document 1.
A light-converging device shown in FIG. 12 is formed of two types of transparent media having different refractive indices and dispersion characteristics (plastic, UV-curing resin, or the like). A lens portion 1 is formed of a first material, and has a lens shape. A grating 1G having a sawteeth-like cross section is formed on a surface 1b, thus presenting a construction similar to that of the lens 1 of FIG. 10. This light-converging device differs from the light-converging device of FIG. 10 in that a transparent layer 7 formed of a second material covers the lens surface 1b on which the grating 1G is formed. A surface 7S of the transparent layer 7 does not reflect the protrusions and depressions of the grating 1G, but has a smooth shape conforming to the lens surface 1b. 
The second material has a higher refractive index and a lower dispersion than those of the first material. As a method for producing the light-converging device, for example, a step of pushing the lens portion 1 (already having the grating 1G formed thereon) into a die, a step of filling the interspace between the lens portion 1 and the die with a second material and subjecting it to UV curing, a step of releasing the die from the lens portion 1, and so on may be consecutively performed.
Light 2 which enters the light-converging device is refracted by the surface 1a of the lens portion 1, and thereafter simultaneously receives refraction and diffraction by the grating 1G. Light 3 going out from the light-converging device is converged on a detection surface 4. Furthermore, when it is transmitted through the surface 7S of the transparent layer 7, it is further refracted so as to be converged on the detection surface 4.
Next, with reference to FIG. 13, the principle of diffraction by the light-converging device shown in FIG. 12 will be described. Again, for simplicity, the face 1a and the face 1b will be described as being planar. It is assumed that the substrate 1 has a refractive index n; the transparent layer 7 has a refractive index n′; and the grating 1G formed on the face 1b has a sawteeth-like cross section with a pitch Λ.
Light 2 of the wavelength λ is diffracted by the grating 1G into 1st-order diffracted light 3, 2nd-order diffracted light 3″, and the like. The relationship between the diffraction directions and the direction of sawteeth is opposite to that associated with the grating 1G shown in FIG. 11. This is because the refractive indices satisfy the relationship n<n′.
Assuming that the incident angle of the light 2 (i.e., the angle between itself and the surface normal) is zero, the diffraction angle θ of qth-order diffracted light (i.e., the angle between itself and the surface normal) is given by (eq. 1) above. In the case of 0th-order light 3′, q=0 and the diffraction angle is zero. Generally speaking, −1st-order diffracted light and −2nd-order diffracted light are also generated on opposite sides of the 0th-order light 3′. However, by adopting a sawteeth-like grating cross section, diffracted light of any − order will be weakened, whereas diffracted light of any + order will be intensified. When a depth d of the grating cross section satisfies (eq. 3) below, the diffraction efficiency of the qth-order diffracted light becomes maximum.d=|qλ/(n′−n)|  (eq. 3)
Note that the pitch Λ does not need to have a constant value. By ensuring that the pitch Λ is a mathematical function of position, it becomes possible to adjust the diffraction angle, and assisted also by the spherical shape of the surfaces 1a and 1b, etc., it becomes possible to converge the diffracted light 3 at one point.    [Non-Patent Document 1] Oyo Hikari Electronics Handbook (published by Shokodo Co., Ltd.), P 474-477    [Patent Document 1] Japanese Laid-Open Patent Publication No. 9-127321